Master Thesis Behavioural Economics Erasmus School of Economics | Erasmus University Rotterdam Bayesian reasoning or heuristics? The effect of time pressure Abstract – Classic economic theories assume that agents make decisions under the beliefs formulated through Bayes’ theorem. However, literature in behavioural economics found that agents used various heuristics to form beliefs. What strategy do agents truly use in Bayesian tasks and what triggers decision makers to change their behaviour? This thesis tested the effect of time limitation on the behaviour of decision makers in Bayesian tasks. We found time pressure decreases the use of Bayesian reasoning and triggered decision makers to switch to the quicker but less accurate heuristics as decision rule. However, the switch did not decrease the average accuracy in the Bayesian tasks due to the low number of Bayesian subject. Author J.P.J. van Gangelen Student Number 511715jg Supervisor Y. Xu First reader Dr. T. Wang Date August 18, 2019 The views stated in this thesis are those of the author and not necessarily those of Erasmus School of Economics or Erasmus University Rotterdam │ Table of contents 1 Introduction ................................................................................................................................... 3 2 Literature review ........................................................................................................................... 5 2.1 Behavioural patterns in Bayesian tasks ................................................................................... 5 2.1.1 Bayesian reasoning .......................................................................................................... 5 2.1.2 Base-rate fallacy .............................................................................................................. 6 2.1.3 Base-rate anchor .............................................................................................................. 7 2.1.4 Prior posterior probability anchor ................................................................................... 8 2.1.5 Incorrect statistical rule ................................................................................................... 8 2.1.6 Random ........................................................................................................................... 9 2.2 Time pressure .......................................................................................................................... 9 2.3 Time pressure and behaviour in Bayesian tasks .................................................................... 11 3 Methodology ................................................................................................................................. 12 3.1 Measure of Bayesian performance ........................................................................................ 12 3.2 Time limitation ...................................................................................................................... 14 3.3 Measures of cognitive ability, motivation, experience and time ........................................... 14 3.4 Demographic question ........................................................................................................... 15 3.5 Monetary incentive ................................................................................................................ 15 3.6 Procedure ............................................................................................................................... 16 4 Results........................................................................................................................................... 17 4.1 Bayesian reasoning performance ........................................................................................... 17 4.1.1 Treatment effect............................................................................................................. 18 4.1.2 Linear regression ........................................................................................................... 19 4.2 Behavioural patterns .............................................................................................................. 21 4.2.1 Identification rules ......................................................................................................... 21 4.2.2 Identified behavioural patterns ...................................................................................... 22 4.3 Demographic statistics .......................................................................................................... 25 5. Discussion and conclusion ........................................................................................................... 25 References ............................................................................................................................................ 29 Appendixes ........................................................................................................................................... 34 Appendix A – Cognitive Reflection Test .......................................................................................... 34 Appendix B – Experiment ................................................................................................................. 35 Appendix C – Test results ................................................................................................................. 42 Appendix D – Behavioural patterns .................................................................................................. 43 2 1 │ Introduction “Doctors are surprisingly bad at reading lab results. It’s putting us all in a risk”. This is the opening of a news article in the Washington Post on October 5th, 2018 (Morgan, 2018). Doctors especially fail to interpret false-positive predictive values, caused by failure in the use of Bayes’ theorem. Research has shown that the majority of medical students, house staff and physicians overestimate a laboratory test result (Manrai, Bhatia, Strymish, Kohane, & Jain, 2014; Casscells, Schoenberger, & Graboys, 1978). Such failures in Bayesian reasoning suggest potentially tragical consequences. According to Brase and Hill (2015) this is a serious, real-world problem. Bayes’ Theorem or Bayes’ rule is a mathematical formula (Figure 1.1) for calculating conditional probabilities, named after the English statistician Thomas Bayes (Bayes, 1764). This basic normative model of information processing is used in economic analysis (Holt & Smith, 2009). 푃(퐵|퐴)푃(퐴) . 01 ∗ .8 푃(퐴|퐵) = .075 = 푃(퐵) . 01 ∗ .8 + .99 ∗ .1 Figure 1.1: Bayes' Theorem (left); Bayes’ theorem applied in mammogram-case (right). A basic Bayesian problem typically contains two levels of information: the base-rate or prior information and the diagnostic or indicant information (Bar-Hillel, 1980). To clarify the theorem, the use will be demonstrated with an example. Suppose, 1% of the female population has breast cancer, this information is called the base-rate. A positive mammogram has a hit rate of 80% and a false alarm rate of 10%. This information is called the diagnostic information. Eddy (1982) asked physicians to estimate the probability that a woman with a positive mammogram actually has breast cancer. In the experiment, 95% of the physicians estimated the probability that she has breast cancer to be between 70% and 80%. Whereas Bayes’ theorem gives a probability of 7.5% (Figure 1.1). This conditional probability is called the posterior probability. A person who acts in line with Bayes’ theorem is called Bayesian. This example shows the importance of correctly combining the base-rate with the diagnostic information. The group of women without breast cancer is much bigger than the group with breast cancer. As a result, the number of false alarm tests is bigger despite the relatively low probability of a false alarm. Bayes’ theorem is pervasively used in economics to describe how an economically fully rational decision maker processes information and forms beliefs. In practice, people do systematically deviate from traditional economic theories of decision-making such as Bayes’ rule. This behaviour can often be explained by heuristics, which can make cognitive biases and economic non-optimal tendencies predictable (Frederiks, Stenner, & Hobman, 2015). Heuristics are efficient cognitive processes to make decisions more quickly or frugally that, conscious or unconscious, ignore part of the information (Gigerenzer & Gaissmaier, 2011). A more accessible but limited way to describe heuristics is to name 3 them mental shortcuts or rule of thumbs (Shah & Oppenheimer, 2008). Gigerenzer and Todd (1999) described the mind as an adaptive toolbox with various heuristics, tailored for specific social and physical environments. The use of heuristics will often result in systematic errors or biases (Tversky & Kahneman, 1974). Heuristics do not help to optimize the decision, rather try to find an option that exceeds an aspiration level. It is impossible to fully analyse each decision in daily life; people do not have unlimited time, mental effort and cognitive ability. Heuristics help to simplify search and decision problems, which allow people to process information in a less effortful way than one would expect from an optimal decision rule (Shah & Oppenheimer, 2008). Not every decision is important enough to spend a load of time and energy, people rather accept